Last summer, I held a job at a local supermarket as a bagger (the person at the end of the counter who bags your items for you and places them in your cart). It wasn't the most riveting job in the world, and after a while I began to amuse myself by paying attention to the items that people bought. By the end of the summer, I'd noticed a few trends in consumption, one of which was very disturbing to me; most of the time, the people who payed using food stamps were the ones buying the unhealthiest foods. And these weren't thin, frail people who looked like they needed all of the calories they could get from a diet consisting primarily of soda, cookies, and frozen dinners: these people looked like people you'd expect to be buying soda, cookies, and frozen dinners.
In a way, it makes sense. Unhealthy food tends to be cheap, rich in calories and instantly ready to eat. For the people in poverty who need to rely on food stamps, this is ideal: they get the most calories per dollar available, and they don't need to spend their (presumably) already very limited time on food preparation.
To me, the correlation between cheap food and unhealthy food seems like structural violence, impeding on impoverished people's well-being needs. Increased levels of obesity among the poor can also lead to other problems; the risk of hospital/health-related bills correlates with obesity, as does a shorter life span. Both of these contribute to the cyclical nature of poverty, as health problems can greatly hinder a person's educational/occupational success. In addition, a new form of cultural violence is born: the fact that the people on food stamps look anything but starved could lead to the mindset that they don't even need the food stamps.

Here are a few articles on the subject that I found:

An article from USAToday, about the correlation between economic and health differences.
http://www.usatoday.com/news/health/2006-05-23-obesity-teens_x.htm

An article from Grist, which is primarily an environmental publication, about the causes of the drop in food prices and the difference between "energy-dense foods" (like Twinkies, for example) and "nutrient-dense foods" (like salmon).
http://www.grist.org/article/philpott7

And this one from Time magazine doesn't have much to do with poverty, but I found it interesting nonetheless. If you're interested in the commercialized agriculture industry and its environmental effects, it's a good read.
http://www.time.com/time/health/article/0,8599,1917458-1,00.html

(Robert's additions) Here's the trailer for the documentary Food, Inc. If you haven't seen it already, I highly recommend it. The documentary touches on the idea of modern agriculture as a form of structural violence. Many of the cheap calories one finds in a grocery store are unhealthy and are cheap because of government subsidies.

Food Inc Trailer

Another insightful documentary on where our food comes from is King Corn. IMO, Food Inc > King Corn, but both are worth seeing. This documentary drives home the message that corn is everywhere in the Standard American Diet (SAD).

King Corn Trailer

Soul Food Junkies, which I mentioned in class, focuses a lot on the limited access to healthy food among low-income populations. In the Q&A session after the 30 minute viewing (the whole documentary is not scheduled to release for another 6-12 months), Hurt emphasized that poor eating habits can be a toll on not only one's physical health, but their emotional health, the emotional health of those around them, and their financial well-being

Soul Food Junkies Trailer

To change things up, here's the blog of a guy who is trying to prove that one can eat a healthy diet on the equivalent of food stamps. For the last two months he and his wife have cut down their spending on food while eating healthy, wholesome meals (warning: what he considers healthy is not exactly what conventional wisdom dictates). He began this project because of films like Food Inc and King Corn portray low-income families as powerless victims of modern agriculture, which was a depiction that he disagreed with.

http://donmatesz.blogspot.com/2010/12/my-meals-122810-more-budget-practically.html
http://donmatesz.blogspot.com/2010/12/primal-or-paleo-on-budget.html